THE USE OF REFERENCE OBJECTIVES IN MULTIOBJECTIVE OPTIMIZATION

THE USE OF REFERENCE OBJECTIVES IN MULTIOBJECTIVE OPTIMIZATION

Springer-Verlag Berlin Heidelberg 1980 | Andrzej P. Wierzbicki
The paper by Andrzej P. Wierzbicki from the International Institute for Applied Systems Analysis explores the use of reference objectives in multiobjective optimization. The main conclusions are: 1. Any point in the objective space, regardless of its attainability or ideal status, can be used to derive scalarizing functions with minima at Pareto points. This approach can be used to develop the entire basic theory of multiobjective optimization, including necessary and sufficient conditions of optimality and the existence of Pareto-optimal solutions. 2. Reference objectives are practical tools for solving various problems such as Pareto-optimality testing, scanning Pareto-optimal solutions, interactive solving of multiobjective problems, group assessment of solutions, and solving dynamic multiobjective optimization problems. The introduction reevaluates the basic assumptions in multicriteria optimization and decision theory from a pragmatical perspective, questioning why highly developed methods are not fully operational in applications. It highlights that individual decisions often involve specific goals or aspiration levels rather than maximizing a utility function. Historical reflections show that while economic theory assumes utility maximization, individual decisions are often guided by reference objectives determined subconsciously. This suggests that utility and value theory may not accurately describe how a single decision is made.The paper by Andrzej P. Wierzbicki from the International Institute for Applied Systems Analysis explores the use of reference objectives in multiobjective optimization. The main conclusions are: 1. Any point in the objective space, regardless of its attainability or ideal status, can be used to derive scalarizing functions with minima at Pareto points. This approach can be used to develop the entire basic theory of multiobjective optimization, including necessary and sufficient conditions of optimality and the existence of Pareto-optimal solutions. 2. Reference objectives are practical tools for solving various problems such as Pareto-optimality testing, scanning Pareto-optimal solutions, interactive solving of multiobjective problems, group assessment of solutions, and solving dynamic multiobjective optimization problems. The introduction reevaluates the basic assumptions in multicriteria optimization and decision theory from a pragmatical perspective, questioning why highly developed methods are not fully operational in applications. It highlights that individual decisions often involve specific goals or aspiration levels rather than maximizing a utility function. Historical reflections show that while economic theory assumes utility maximization, individual decisions are often guided by reference objectives determined subconsciously. This suggests that utility and value theory may not accurately describe how a single decision is made.
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